12AH vs 14AH vs 18AH

Wasn't quite sure where to post this, new to the site, but figured as I have what I would consider a small scooter I'd post my question here.

Basically put, I baught a used scooter, 4x12voltx12AH-500watt.
It worked great for a few weeks, this morning, went into the garage to head off to work and I smelled rotten eggs, tried to take off with the scooter, got absolutely nothing!
So I put the bike back up on it's centre stand and twisted the throttle. The tire started to spin about 3 rotations per minute studdering and the battery meter read DEAD!
Not impressed. So this evening I took apart the battery case to find my batteries were all melted. Each of the 4 batteries was deforemed, warped, bulged. Brutal!

Now not quite sure exactly why it happened. But I have a few theories. 1. It started with previous owner, I killed them totally. 2. Charging it right after a 20-30 minute ride. 3.I have a wire behind my headlight, not sure exactly what it does but when it is connected the bike will only do 20km/h. When I disconnect it, I get up to 35-38km/h. So obviously as I like speed, at least faster than crawling, I have been riding with the wire unplugged. Never had a problem until this morning.

So now I need some replacement batteries. I am curious if it is due to the wire being unplugged, lets call it my limiter wire, then is there any way I can prevent this from happening with the new batteries?

Also with the new batteries, I found 12volt, 12ah batteries which will fit in my battery case, but I also found 12vold 14ah, as well as 12volt 18ah batteries that all match the measurements of the old batteries(before deforming).

I am curious as to what I should put in? Should I stick with what was there and replace them with 12volt 12ah batteries, or would I receive either more speed/distance with using 14ah or 18ah batteries?

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Wow, that's some nasty meltage!! You wont gain more speed by replacing the 4 batteries with another 4, voltage will be the same, but, better batteries may give you better performance in both Length of run and power. Main thing is , to get batteries specifically designed for Electric Vehicles so they can take the abuse they will get under normal use. (some batteries despite the same V and Ah ratings are designed for low current draw over extended times, rather than a high current draw for a shorter time) Higher Ah ratings translates to longer distance travelled. I'm not too sure I'd trust that charger either, even if there was a problem with the batteries to start with.